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AM-22 - Global Measures of Spatial Association

Spatial association broadly describes how the locations and values of samples or observations vary across space. Similarity in both the attribute values and locations of observations can be assessed using measures of spatial association based upon the first law of geography. In this entry, we focus on the measures of spatial autocorrelation that assess the degree of similarity between attribute values of nearby observations across the entire study region. These global measures assess spatial relationships with the combination of spatial proximity as captured in the spatial weights matrix and the attribute similarity as captured by variable covariance (i.e. Moran’s I) or squared difference (i.e. Geary’s C). For categorical data, the join count statistic provides a global measure of spatial association. Two visualization approaches for spatial autocorrelation measures include Moran scatterplots and variograms (also known as semi-variograms).

AM-90 - Computational Movement Analysis

Figure 1. Group movement patterns as illustrated in this coordinated escape behavior of a group of mountain goat (Rubicapra rubicapra) evading approaching hikers on the Fuorcla Trupchun near the Italian/Swiss border are at the core of computational movement analysis. Once the trajectories of moving objects are collected and made accessible for computational processing, CMA aims at a better understanding of the characteristics of movement processes of animals, people or things in geographic space.


Computational Movement Analysis (CMA) develops and applies analytical computational tools aiming at a better understanding of movement data. CMA copes with the rapidly growing data streams capturing the mobility of people, animals, and things roaming geographic spaces. CMA studies how movement can be represented, modeled, and analyzed in GIS&T. The CMA toolbox includes a wide variety of approaches, ranging from database research, over computational geometry to data mining and visual analytics.

AM-34 - The Geographically Weighted Regression Framework

Local multivariate statistical models are increasingly encountered in geographical research to estimate spatially varying relationships between a response variable and its associated predictor variables. In geography and many other disciplines, such models have been largely embedded within the framework of regression and can reveal significantly more information about the determinants of observed spatial distribution of the dependent variable than their global regression model counterparts. This section introduces one type of local statistical modeling framework: Geographically Weighted Regression (GWR). Models within this framework estimate location-specific parameter estimates for each covariate, local diagnostic statistics, and bandwidth parameters as indicators of the spatial scales at which the modeled processes operate. These models provide an effective means to estimate how the same factors may evoke different responses across locations and by so doing, bring to the fore the role of geographical context on human preferences and behavior.

AM-29 - Kriging Interpolation

Kriging is an interpolation method that makes predictions at unsampled locations using a linear combination of observations at nearby sampled locations. The influence of each observation on the kriging prediction is based on several factors: 1) its geographical proximity to the unsampled location, 2) the spatial arrangement of all observations (i.e., data configuration, such as clustering of observations in oversampled areas), and 3) the pattern of spatial correlation of the data. The development of kriging models is meaningful only when data are spatially correlated.. Kriging has several advantages over traditional interpolation techniques, such as inverse distance weighting or nearest neighbor: 1) it provides a measure of uncertainty attached to the results (i.e., kriging variance); 2) it accounts for direction-dependent relationships (i.e., spatial anisotropy); 3) weights are assigned to observations based on the spatial correlation of data instead of assumptions made by the analyst for IDW; 4) kriging predictions are not constrained to the range of observations used for interpolation, and 5) data measured over different spatial supports can be combined and change of support, such as downscaling or upscaling, can be conducted.

AM-20 - Geospatial Analysis and Model Building

Spatial modeling is an important instrument to conduct geospatial analysis to understand the world and guide decision-making. In GIS, spatial models are formal languages to express mechanisms of geographic processes and design analytical workflows to understand these processes. With the development of GIS and computer science, various types of spatial models and modeling techniques have become available, which endows the term of “spatial model” with different meanings. This entry provides an overview of common types of spatial models, modeling techniques, and related applications.

AM-54 - Landscape Metrics

Landscape metrics are algorithms that quantify the spatial structure of patterns – primarily composition and configuration - within a geographic area. The term "landscape metrics" has historically referred to indices for categorical land cover maps, but with emerging datasets, tools, and software programs, the field is growing to include other types of landscape pattern analyses such as graph-based metrics, surface metrics, and three-dimensional metrics. The choice of which metrics to use requires careful consideration by the analyst, taking into account the data and application. Selecting the best metric for the problem at hand is not a trivial task given the large numbers of metrics that have been developed and software programs to implement them.

CV-24 - User-Centered Design and Evaluation
  • Describe the baseline expectations that a particular map makes of its audience
  • Compare and contrast the interpretive dangers (e.g., ecological fallacy, Modifiable Areal Unit Problem) that are inherent to different types of maps or visualizations and their underlying geographic data
  • Identify several uses for which a particular map is or is not effective
  • Identify the particular design choices that make a map more or less effective
  • Evaluate the effectiveness of a map for its audience and purpose
  • Design a testing protocol to evaluate the usability of a simple graphical user interface
  • Perform a rigorous sampled field check of the accuracy of a map
  • Discuss the use limitations of the USGS map accuracy standards for a range of projects demanding different levels of precision (e.g., driving directions vs. excavation planning)
AM-10 - Spatial Interaction

Spatial interaction (SI) is a fundamental concept in the GIScience literature, and may be defined in numerous ways. SI often describes the "flow" of individuals, commodities, capital, and information over (geographic) space resulting from a decision process. Alternatively, SI is sometimes used to refer to the influence of spatial proximity of places on the intensity of relations between those places. SI modeling as a separate research endeavor developed out of a need to mathematically model and understand the underlying determinants of these flows/influences. Proponents of SI modeling include economic geographers, regional scientists, and regional planners, as well as climate scientists, physicists, animal ecologists, and even some biophysical/environmental researchers. Originally developed from theories of interacting particles and gravitational forces in physics, SI modeling has developed through a series of refinements in terms of functional form, conceptual representations of distances, as well as a range of analytically rigorous technical improvements.

AM-68 - Rule Learning for Spatial Data Mining

Recent research has identified rule learning as a promising technique for geographic pattern mining and knowledge discovery to make sense of the big spatial data avalanche (Koperski & Han, 1995; Shekhar et al., 2003). Rules conveying associative implications regarding locations, as well as semantic and spatial characteristics of analyzed spatial features, are especially of interest. This overview considers fundamentals and recent advancements in two approaches applied on spatial data: spatial association rule learning and co-location rule learning.

AM-38 - Pattern Recognition and Matching

People recognize and characterize patterns to understand the world. Spatial data exhibit distinctive characteristics that render most aspatial recognition and matching methods unsuitable or inefficient. In past decades, a plethora of methods have been developed for spatial pattern recognition and matching to account for these spatial characteristics. This entry first focuses on the methods of spatial pattern recognition, including an overview of the basic concepts and common  types. Methods for spatial pattern matching are then introduced. An example scenario of the distribution of tree species in the Arbuckle Mountains of south-central Oklahoma illustrates covered concepts. The entry concludes with brief remarks on continuing challenges and future directions in spatial pattern recognition and matching in the Big Data and artificial intelligence era.